Block #515,613

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2014, 9:39:35 PM · Difficulty 10.8420 · 6,310,956 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

85acc379f78eb8eb78a457dc54c92a781be49a09a47bd0aa4f890242e5618bc9

View on Chainz ↗

Height

#515,613

Difficulty

10.842015

Transactions

Size

1.23 KB

Version

Bits

0ad78e44

Nonce

30,154,323

Timestamp

4/28/2014, 9:39:35 PM

Confirmations

6,310,956

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

bbc4992706ab2babeae2d368d70b5589ace0adafc9aaba1bc4661ee0eb3d0c39

Transactions (5)

Coinbase962f9c3d39bcf8…69b57912aec0ab

1 in → 1 out8.5300 XPM116 B

AbwWkWZt…kawDhufa

8a1ef81d736ccf…26d7a5931cde25

1 in → 2 out6.4651 XPM226 B

AWNcv4XD…RttjY2gH AG4jgfQm…4ssLmUJU

fe89770a716df9…a7f18845b5558c

1 in → 2 out5.4182 XPM226 B

AXDWcx53…FrtY2diY AN49h7KL…YwBzJu4V

0d8b26b799a627…b7c223aa206871

1 in → 2 out1.7721 XPM226 B

AbrWgxq6…cbchKH5j AG8u7ddV…cU5QJSqk

33063a657df7ba…8acef26a7ff634

2 in → 2 out5.1141 XPM374 B

AZoEnnQD…5GicVHBE AdahuLtL…CbNyF5MW

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.

2.737 × 10⁹⁹(100-digit number)

27373875179984502344…22354671251312702399

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

2.737 × 10⁹⁹(100-digit number)

27373875179984502344…22354671251312702399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.737 × 10⁹⁹(100-digit number)

27373875179984502344…22354671251312702401

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

5.474 × 10⁹⁹(100-digit number)

54747750359969004688…44709342502625404799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.474 × 10⁹⁹(100-digit number)

54747750359969004688…44709342502625404801

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

1.094 × 10¹⁰⁰(101-digit number)

10949550071993800937…89418685005250809599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.094 × 10¹⁰⁰(101-digit number)

10949550071993800937…89418685005250809601

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

2.189 × 10¹⁰⁰(101-digit number)

21899100143987601875…78837370010501619199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.189 × 10¹⁰⁰(101-digit number)

21899100143987601875…78837370010501619201

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

4.379 × 10¹⁰⁰(101-digit number)

43798200287975203751…57674740021003238399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.379 × 10¹⁰⁰(101-digit number)

43798200287975203751…57674740021003238401

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

8.759 × 10¹⁰⁰(101-digit number)

87596400575950407502…15349480042006476799

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #515,613

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