Block #127,570

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/21/2013, 2:58:26 PM · Difficulty 9.7841 · 6,682,796 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

34014d3e4447ef022755e19492cc31ab4007857b63155ca6766133a834b4d934

View on Chainz ↗

Height

#127,570

Difficulty

9.784102

Transactions

Size

428 B

Version

Bits

09c8baea

Nonce

148,894

Timestamp

8/21/2013, 2:58:26 PM

Confirmations

6,682,796

Mined by

⛏️ P2SHAWBAtu2YB4tzQF7YEXLWRnR9mFtgHoE1Qc

Merkle Root

430a5d3ba609909b90f96ce7afa0a5e722034d9ef31731fd5bb5492ec71402a5

Transactions (2)

Coinbase7e987d7dc8fe4d…8ff528c01302ed

1 in → 1 out10.4400 XPM109 B

AWBAtu2Y…tgHoE1Qc

e32a482796a04f…67be95a674346c

1 in → 2 out8.4300 XPM227 B

AGZvBxxa…shhkwtTn AXwKtmuu…YzxfsWPW

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.

1.354 × 10¹⁰⁰(101-digit number)

13542524527871879967…40407806236228124039

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

1.354 × 10¹⁰⁰(101-digit number)

13542524527871879967…40407806236228124039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.354 × 10¹⁰⁰(101-digit number)

13542524527871879967…40407806236228124041

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

2.708 × 10¹⁰⁰(101-digit number)

27085049055743759934…80815612472456248079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.708 × 10¹⁰⁰(101-digit number)

27085049055743759934…80815612472456248081

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

5.417 × 10¹⁰⁰(101-digit number)

54170098111487519869…61631224944912496159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.417 × 10¹⁰⁰(101-digit number)

54170098111487519869…61631224944912496161

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

1.083 × 10¹⁰¹(102-digit number)

10834019622297503973…23262449889824992319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.083 × 10¹⁰¹(102-digit number)

10834019622297503973…23262449889824992321

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

2.166 × 10¹⁰¹(102-digit number)

21668039244595007947…46524899779649984639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #127,570

Cookie Preferences