Block #1,554,229

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2016, 2:26:29 PM · Difficulty 10.6585 · 5,279,616 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

965667c29b83a149ab403e4115abe836724b4528fccae4d29ca96fd1c56614df

View on Chainz ↗

Height

#1,554,229

Difficulty

10.658472

Transactions

Size

2.48 KB

Version

Bits

0aa8919c

Nonce

990,028,930

Timestamp

4/23/2016, 2:26:29 PM

Confirmations

5,279,616

Mined by

⛏️ P2SHAMHb9d3WwYdW5Jd1HLctZKBQptxMtcGurq

Merkle Root

b50c0724e35cfecc92b4609f47e5a0af004c71410e555533ef43d040f7984a5d

Transactions (2)

Coinbasead4af28932d559…34b70cabf782fa

1 in → 1 out8.8200 XPM110 B

AMHb9d3W…xMtcGurq

e02f741a6a1bff…cf2b90e40b4436

4 in → 51 out8.5757 XPM2.28 KB

AaVTBaH5…XU1JJ57s AZ3cZHxS…1qdoLqba AHeceAvC…KYvwjQQR AGuTJSAq…dxwfxpkt AamuTW2d…WVcmebZa

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.

5.642 × 10⁹³(94-digit number)

56420707769631529224…11010294235901017699

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

5.642 × 10⁹³(94-digit number)

56420707769631529224…11010294235901017699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.642 × 10⁹³(94-digit number)

56420707769631529224…11010294235901017701

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

1.128 × 10⁹⁴(95-digit number)

11284141553926305844…22020588471802035399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.128 × 10⁹⁴(95-digit number)

11284141553926305844…22020588471802035401

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

2.256 × 10⁹⁴(95-digit number)

22568283107852611689…44041176943604070799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.256 × 10⁹⁴(95-digit number)

22568283107852611689…44041176943604070801

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

4.513 × 10⁹⁴(95-digit number)

45136566215705223379…88082353887208141599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.513 × 10⁹⁴(95-digit number)

45136566215705223379…88082353887208141601

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

9.027 × 10⁹⁴(95-digit number)

90273132431410446759…76164707774416283199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.027 × 10⁹⁴(95-digit number)

90273132431410446759…76164707774416283201

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 #1,554,229

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