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Home/Chain Registry/Block #2,829,137

Block #2,829,137

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/7/2018, 7:26:59 PM Β· Difficulty 11.7118 Β· 4,011,117 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
587b34b3b5fd02aff055fbae175d4c356383b75a371b5edf0e0a982b0d1a5edc
View on Chainz β†—

Difficulty

11.711774

Transactions

1

Size

200 B

Version

2

Bits

0bb636d8

Nonce

390,090,071

Timestamp

9/7/2018, 7:26:59 PM

Confirmations

4,011,117

Merkle Root

3b36d32089c962dce87eb0de69d7af0055a5d0007bdd659e9d097ebef4c03642
Transactions (1)
Coinbase3b36d32089c962…097ebef4c03642
1 in β†’ 1 out7.2800 XPM110 B
AMyLg76K…UTquzu3j
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.

5.198 Γ— 10⁹⁴(95-digit number)
51985995025495959775…67938172840800136920
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
5.198 Γ— 10⁹⁴(95-digit number)
51985995025495959775…67938172840800136919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.198 Γ— 10⁹⁴(95-digit number)
51985995025495959775…67938172840800136921
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
1.039 Γ— 10⁹⁡(96-digit number)
10397199005099191955…35876345681600273839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.039 Γ— 10⁹⁡(96-digit number)
10397199005099191955…35876345681600273841
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
2.079 Γ— 10⁹⁡(96-digit number)
20794398010198383910…71752691363200547679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.079 Γ— 10⁹⁡(96-digit number)
20794398010198383910…71752691363200547681
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
4.158 Γ— 10⁹⁡(96-digit number)
41588796020396767820…43505382726401095359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.158 Γ— 10⁹⁡(96-digit number)
41588796020396767820…43505382726401095361
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
8.317 Γ— 10⁹⁡(96-digit number)
83177592040793535641…87010765452802190719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.317 Γ— 10⁹⁡(96-digit number)
83177592040793535641…87010765452802190721
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
1.663 Γ— 10⁹⁢(97-digit number)
16635518408158707128…74021530905604381439
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 2829137

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 587b34b3b5fd02aff055fbae175d4c356383b75a371b5edf0e0a982b0d1a5edc

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 #2,829,137 on Chainz β†—
Circulating Supply:57,966,347 XPMΒ·at block #6,840,253 Β· updates every 60s
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