Block #358,279

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2014, 11:35:41 PM · Difficulty 10.3883 · 6,448,138 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86cd6ee76690dd1f72b692cfc3960b71fdf0406cae1271a4a2b0514b3868370b

View on Chainz ↗

Height

#358,279

Difficulty

10.388336

Transactions

Size

1.94 KB

Version

Bits

0a6369f6

Nonce

16,690

Timestamp

1/13/2014, 11:35:41 PM

Confirmations

6,448,138

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

240d9b11993733507f53697a66e58e68d7dfc2e5d13ac33802e11e49d1baad4f

Transactions (3)

Coinbasebcba39714d1949…13cc98ec9f7e9c

1 in → 2 out9.2800 XPM137 B

ARmAMwyu…P7Kn74ZT AU6kq4CL…dQBLvxLp

3fd71ad57e16be…68e5ff0539c0fd

6 in → 15 out47.6968 XPM1.21 KB

ALXni592…rFt26Kdr AKLedcpa…h7KX6VkY AY6cP2c9…aCBvj3TK AYdPHLt1…MxqQxULs APJ3F9Bt…hRmbyT7p

dfa894df8437dd…c81d6f076f175f

3 in → 2 out2.0668 XPM521 B

AGyhc9Ym…YqF23X8n AHSryiXP…Qrv7BCLy

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.

1.208 × 10¹⁰¹(102-digit number)

12082067328992800645…31869883190741441679

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

1.208 × 10¹⁰¹(102-digit number)

12082067328992800645…31869883190741441679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.208 × 10¹⁰¹(102-digit number)

12082067328992800645…31869883190741441681

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

2.416 × 10¹⁰¹(102-digit number)

24164134657985601290…63739766381482883359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.416 × 10¹⁰¹(102-digit number)

24164134657985601290…63739766381482883361

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

4.832 × 10¹⁰¹(102-digit number)

48328269315971202581…27479532762965766719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.832 × 10¹⁰¹(102-digit number)

48328269315971202581…27479532762965766721

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

9.665 × 10¹⁰¹(102-digit number)

96656538631942405162…54959065525931533439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.665 × 10¹⁰¹(102-digit number)

96656538631942405162…54959065525931533441

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

1.933 × 10¹⁰²(103-digit number)

19331307726388481032…09918131051863066879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.933 × 10¹⁰²(103-digit number)

19331307726388481032…09918131051863066881

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

Block #358,279

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