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Home/Chain Registry/Block #3,156,327

Block #3,156,327

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/26/2019, 1:20:45 PM Β· Difficulty 11.3200 Β· 3,677,635 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
136951c80b243a11e1ba5d411764773ff09ca98f8e51ad29b51f00f855e6008d
View on Chainz β†—

Difficulty

11.320012

Transactions

2

Size

2.44 KB

Version

2

Bits

0b51ec54

Nonce

1,206,264,536

Timestamp

4/26/2019, 1:20:45 PM

Confirmations

3,677,635

Merkle Root

7f5093f2f31887c726bbfccbc29a80bbc0f05eba903fdcc602b9190c24aeee7b
Transactions (2)
Coinbase3549e7c9811e7a…11a4652c8fbefe
1 in β†’ 1 out7.8300 XPM110 B
ARbm48qR…9xQc8DBX
95675b86e7cb6d…eb3bbb5f955887
15 in β†’ 2 out1072.4286 XPM2.25 KB
AQpirNZH…YMX3K11gAQsmTAaA…pbc2UKCq
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.913 Γ— 10⁹⁴(95-digit number)
19132101480265920336…56235300076329021650
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.913 Γ— 10⁹⁴(95-digit number)
19132101480265920336…56235300076329021649
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.913 Γ— 10⁹⁴(95-digit number)
19132101480265920336…56235300076329021651
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.826 Γ— 10⁹⁴(95-digit number)
38264202960531840673…12470600152658043299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.826 Γ— 10⁹⁴(95-digit number)
38264202960531840673…12470600152658043301
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
7.652 Γ— 10⁹⁴(95-digit number)
76528405921063681346…24941200305316086599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.652 Γ— 10⁹⁴(95-digit number)
76528405921063681346…24941200305316086601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.530 Γ— 10⁹⁡(96-digit number)
15305681184212736269…49882400610632173199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.530 Γ— 10⁹⁡(96-digit number)
15305681184212736269…49882400610632173201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.061 Γ— 10⁹⁡(96-digit number)
30611362368425472538…99764801221264346399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.061 Γ— 10⁹⁡(96-digit number)
30611362368425472538…99764801221264346401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.122 Γ— 10⁹⁡(96-digit number)
61222724736850945076…99529602442528692799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 3156327

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 136951c80b243a11e1ba5d411764773ff09ca98f8e51ad29b51f00f855e6008d

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #3,156,327 on Chainz β†—
Circulating Supply:57,915,925 XPMΒ·at block #6,833,961 Β· updates every 60s
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