Block #550,988

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/18/2014, 12:45:53 PM · Difficulty 10.9621 · 6,263,527 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5d66d4643298337fddf714d73f379f2ae9f1395782dabae2d21b90477ef251d5

View on Chainz ↗

Height

#550,988

Difficulty

10.962114

Transactions

Size

1.19 KB

Version

Bits

0af64d16

Nonce

764,610,767

Timestamp

5/18/2014, 12:45:53 PM

Confirmations

6,263,527

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a53f35fba94a27623e702caa4628645ccece3d12fcb17105173f32dec904a685

Transactions (4)

Coinbase098b6305204f5e…aa10ca64adff22

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

6d7233d5577920…f796c93776d5ea

3 in → 3 out6.6616 XPM556 B

AT84m5QM…XEF1yxxC AeKNrjNj…1NEq95Ta ASH3HaLZ…1LTAJLUm

3029356346d358…afd665bd8a6522

1 in → 2 out1.4670 XPM225 B

Acr4YSYp…psvNUAqV ANGJYZkp…sBJVintj

621e15c9d2e2d1…3d0dcf3dd3e2bf

1 in → 2 out1.1680 XPM227 B

AR57wig1…YwqXKhMy ALZN8nKT…JK7qVZhw

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 × 10¹⁰⁰(101-digit number)

12083591836927133961…70112159612291768319

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 × 10¹⁰⁰(101-digit number)

12083591836927133961…70112159612291768319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.208 × 10¹⁰⁰(101-digit number)

12083591836927133961…70112159612291768321

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 × 10¹⁰⁰(101-digit number)

24167183673854267923…40224319224583536639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.416 × 10¹⁰⁰(101-digit number)

24167183673854267923…40224319224583536641

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

4.833 × 10¹⁰⁰(101-digit number)

48334367347708535847…80448638449167073279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.833 × 10¹⁰⁰(101-digit number)

48334367347708535847…80448638449167073281

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

9.666 × 10¹⁰⁰(101-digit number)

96668734695417071695…60897276898334146559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.666 × 10¹⁰⁰(101-digit number)

96668734695417071695…60897276898334146561

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 × 10¹⁰¹(102-digit number)

19333746939083414339…21794553796668293119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.933 × 10¹⁰¹(102-digit number)

19333746939083414339…21794553796668293121

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 #550,988

Cookie Preferences