Block #879,437

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2015, 4:33:19 PM · Difficulty 10.9625 · 5,951,203 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b11fe43cbf0f9d25726bd4f6c05bc2940ef24f8e2d2595f5c0cacb7d9bed707

View on Chainz ↗

Height

#879,437

Difficulty

10.962517

Transactions

Size

1.67 KB

Version

Bits

0af6677d

Nonce

2,173,638,966

Timestamp

1/2/2015, 4:33:19 PM

Confirmations

5,951,203

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f7b04ebffe83d55f86b0c325f67dd8249385908e3fd10b353d066ce62dd2798c

Transactions (5)

Coinbase1c8d9eb3a5f774…701d998e63b477

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

174c30f6550a79…5a27e4e51c83c2

5 in → 2 out20.4904 XPM818 B

ALtt5pM7…xLVVZkZN ANZEUG5r…frJ8qk9b

46f913617dec5b…47e7633d894316

1 in → 2 out6.0935 XPM226 B

AL7B788G…ntju5878 AYJiZwHb…HbufPs8B

faddd6209e4f3c…b180921758cb9a

1 in → 2 out2.8006 XPM226 B

ALP6szJY…eEPSo5sX AHhZ4F5T…SUAgByF8

807e60eeb12a1c…f27d1bfd01e255

1 in → 2 out4.2057 XPM227 B

Abh9BL3k…mri2E9bU AHRoBSh4…BSVTQ36Q

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.

1.270 × 10¹⁰⁰(101-digit number)

12709703925499405443…38222439711132221439

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

1.270 × 10¹⁰⁰(101-digit number)

12709703925499405443…38222439711132221439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.270 × 10¹⁰⁰(101-digit number)

12709703925499405443…38222439711132221441

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

2.541 × 10¹⁰⁰(101-digit number)

25419407850998810886…76444879422264442879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.541 × 10¹⁰⁰(101-digit number)

25419407850998810886…76444879422264442881

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

5.083 × 10¹⁰⁰(101-digit number)

50838815701997621773…52889758844528885759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.083 × 10¹⁰⁰(101-digit number)

50838815701997621773…52889758844528885761

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

1.016 × 10¹⁰¹(102-digit number)

10167763140399524354…05779517689057771519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.016 × 10¹⁰¹(102-digit number)

10167763140399524354…05779517689057771521

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

2.033 × 10¹⁰¹(102-digit number)

20335526280799048709…11559035378115543039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.033 × 10¹⁰¹(102-digit number)

20335526280799048709…11559035378115543041

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 #879,437

Cookie Preferences