Block #546,881

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/16/2014, 3:16:53 AM · Difficulty 10.9567 · 6,258,474 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2a4c942c70c8f1c6cd7ad6932d58a02fdd4fbc945d2165546c45739a4f8345bb

View on Chainz ↗

Height

#546,881

Difficulty

10.956698

Transactions

Size

662 B

Version

Bits

0af4ea2d

Nonce

351,439,831

Timestamp

5/16/2014, 3:16:53 AM

Confirmations

6,258,474

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

24090d6e7b5d9a9e713a40e16d41caa80be810fdb2ce0352902cc3cd48fee350

Transactions (3)

Coinbase3047070f3cecc3…98b5d1e42575d0

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

073b9b0437333e…9492fe9dfb72bb

1 in → 2 out5.3246 XPM226 B

AaSUNzJU…2iWckcUK AeKNrjNj…1NEq95Ta

fbca6c37b0841d…5698d3939b7ef3

1 in → 2 out1.6164 XPM227 B

AHU3ZAYi…E4grhoYJ APNA1QFw…sK1RroHX

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.

7.222 × 10¹⁰⁰(101-digit number)

72228785596421490797…54712452685074022399

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

7.222 × 10¹⁰⁰(101-digit number)

72228785596421490797…54712452685074022399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.222 × 10¹⁰⁰(101-digit number)

72228785596421490797…54712452685074022401

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

1.444 × 10¹⁰¹(102-digit number)

14445757119284298159…09424905370148044799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.444 × 10¹⁰¹(102-digit number)

14445757119284298159…09424905370148044801

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

2.889 × 10¹⁰¹(102-digit number)

28891514238568596318…18849810740296089599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.889 × 10¹⁰¹(102-digit number)

28891514238568596318…18849810740296089601

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

5.778 × 10¹⁰¹(102-digit number)

57783028477137192637…37699621480592179199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.778 × 10¹⁰¹(102-digit number)

57783028477137192637…37699621480592179201

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

1.155 × 10¹⁰²(103-digit number)

11556605695427438527…75399242961184358399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.155 × 10¹⁰²(103-digit number)

11556605695427438527…75399242961184358401

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