Block #315,774

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2013, 4:48:26 PM · Difficulty 10.1144 · 6,480,290 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2fc0d85d03e3725c047ffce1ae8527ab736083bbe53773ecef603c80dbb2cbeb

View on Chainz ↗

Height

#315,774

Difficulty

10.114386

Transactions

Size

877 B

Version

Bits

0a1d4866

Nonce

43,507

Timestamp

12/16/2013, 4:48:26 PM

Confirmations

6,480,290

Mined by

⛏️ P2SHAMVjXKhng52v6S6tdBCyzY1qteH3RSh931

Merkle Root

9ce391473f32a3b2b94425b89c30859128f90f393f51c12f2c1b9d1ffd709cc8

Transactions (4)

Coinbasef2d1ff53a9d65d…a92a29e4cf6cab

1 in → 1 out9.7900 XPM109 B

AMVjXKhn…H3RSh931

2282929098e7d9…dd7311e6f7a0f0

1 in → 2 out6.9267 XPM226 B

AHu9p6rz…2SJ2K6as Acc88UD6…qmTPBCC6

91ce66c2b77bf7…55d074eb954105

1 in → 2 out5.8991 XPM225 B

AHCqnq5e…egZS4U4X AdXGhyra…onrZTeuK

77e812b59c7439…be806dcc5612a7

1 in → 2 out6.9180 XPM226 B

AeGkrx8m…V3akuHL7 AUmvmfPf…byz4ouUr

Prime Chain Origin

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

5.918 × 10⁹⁶(97-digit number)

59182725902272323202…97045394083058307839

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

5.918 × 10⁹⁶(97-digit number)

59182725902272323202…97045394083058307839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.918 × 10⁹⁶(97-digit number)

59182725902272323202…97045394083058307841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.183 × 10⁹⁷(98-digit number)

11836545180454464640…94090788166116615679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.183 × 10⁹⁷(98-digit number)

11836545180454464640…94090788166116615681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.367 × 10⁹⁷(98-digit number)

23673090360908929281…88181576332233231359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.367 × 10⁹⁷(98-digit number)

23673090360908929281…88181576332233231361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

4.734 × 10⁹⁷(98-digit number)

47346180721817858562…76363152664466462719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.734 × 10⁹⁷(98-digit number)

47346180721817858562…76363152664466462721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

9.469 × 10⁹⁷(98-digit number)

94692361443635717124…52726305328932925439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.469 × 10⁹⁷(98-digit number)

94692361443635717124…52726305328932925441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer