Block #856,118

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 12/16/2014, 8:26:06 PM · Difficulty 10.9682 · 5,987,713 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f5b407a7eab4fecfc7deb9f4449621b8e7e0503c42b3a339582fc1e545cc6350

View on Chainz ↗

Height

#856,118

Difficulty

10.968196

Transactions

Size

657 B

Version

Bits

0af7dbb9

Nonce

408,394,355

Timestamp

12/16/2014, 8:26:06 PM

Confirmations

5,987,713

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8928d324f12132919bd497b21f03fb7b4517023c26b48fe2cb15c76f495f00c0

Transactions (3)

Coinbased8980777b0e392…151ae70a444d68

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

3f1bbcc170c61d…c6dbd78116afcf

1 in → 2 out0.0906 XPM225 B

AScpSCRk…LtetqECN AL6XXNjj…7i2L5Lpu

1860fb4fa37ee2…27d91f82861af3

1 in → 2 out0.0903 XPM225 B

AR7RywaA…3gEDbu89 AZ5Ta7AM…vWYcnXY5

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.

5.908 × 10⁹⁶(97-digit number)

59082463076118039534…17598908008038369279

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

5.908 × 10⁹⁶(97-digit number)

59082463076118039534…17598908008038369279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.908 × 10⁹⁶(97-digit number)

59082463076118039534…17598908008038369281

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

1.181 × 10⁹⁷(98-digit number)

11816492615223607906…35197816016076738559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.181 × 10⁹⁷(98-digit number)

11816492615223607906…35197816016076738561

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

2.363 × 10⁹⁷(98-digit number)

23632985230447215813…70395632032153477119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.363 × 10⁹⁷(98-digit number)

23632985230447215813…70395632032153477121

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

4.726 × 10⁹⁷(98-digit number)

47265970460894431627…40791264064306954239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.726 × 10⁹⁷(98-digit number)

47265970460894431627…40791264064306954241

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

9.453 × 10⁹⁷(98-digit number)

94531940921788863255…81582528128613908479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.453 × 10⁹⁷(98-digit number)

94531940921788863255…81582528128613908481

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.890 × 10⁹⁸(99-digit number)

18906388184357772651…63165056257227816959

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.890 × 10⁹⁸(99-digit number)

18906388184357772651…63165056257227816961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #856,118

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