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Home/Chain Registry/Block #1,357,947

Block #1,357,947

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/6/2015, 6:06:46 PM Β· Difficulty 10.8296 Β· 5,468,682 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8c37dab07ebb13d44a17fae80c0eece201e383015a64053a4c8f7d11cf2deb98
View on Chainz β†—

Difficulty

10.829582

Transactions

1

Size

201 B

Version

2

Bits

0ad45f7c

Nonce

1,927,110,405

Timestamp

12/6/2015, 6:06:46 PM

Confirmations

5,468,682

Merkle Root

15b8f19b40a885a54ae8d6d08512b5c2bd50045c9204d85dd2191767380fe346
Transactions (1)
Coinbase15b8f19b40a885…191767380fe346
1 in β†’ 1 out8.5100 XPM110 B
AZTKyTRu…pyfuTZVc
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.

1.698 Γ— 10⁹⁷(98-digit number)
16987266855769450204…36535832559884185600
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
1.698 Γ— 10⁹⁷(98-digit number)
16987266855769450204…36535832559884185599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.698 Γ— 10⁹⁷(98-digit number)
16987266855769450204…36535832559884185601
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
3.397 Γ— 10⁹⁷(98-digit number)
33974533711538900408…73071665119768371199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.397 Γ— 10⁹⁷(98-digit number)
33974533711538900408…73071665119768371201
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
6.794 Γ— 10⁹⁷(98-digit number)
67949067423077800817…46143330239536742399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.794 Γ— 10⁹⁷(98-digit number)
67949067423077800817…46143330239536742401
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
1.358 Γ— 10⁹⁸(99-digit number)
13589813484615560163…92286660479073484799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.358 Γ— 10⁹⁸(99-digit number)
13589813484615560163…92286660479073484801
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
2.717 Γ— 10⁹⁸(99-digit number)
27179626969231120326…84573320958146969599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.717 Γ— 10⁹⁸(99-digit number)
27179626969231120326…84573320958146969601
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
5.435 Γ— 10⁹⁸(99-digit number)
54359253938462240653…69146641916293939199
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 1357947

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 8c37dab07ebb13d44a17fae80c0eece201e383015a64053a4c8f7d11cf2deb98

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 #1,357,947 on Chainz β†—
Circulating Supply:57,857,177 XPMΒ·at block #6,826,628 Β· updates every 60s
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