Block #1,070,514

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/22/2015, 8:00:22 AM · Difficulty 10.7427 · 5,721,304 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bdee5d3cf66a81a63fd05169c6392f82b6b49d41e1bfbf9f787e4e103e7a3e29

View on Chainz ↗

Height

#1,070,514

Difficulty

10.742674

Transactions

Size

1.23 KB

Version

Bits

0abe1fe8

Nonce

914,026,678

Timestamp

5/22/2015, 8:00:22 AM

Confirmations

5,721,304

Merkle Root

5e004f4ada63c40a9404ccc01935d78df3d12e3c682af564503d05b0ced651f1

Transactions (5)

Coinbaseb6a21f182404b4…dd0c279255826a

1 in → 1 out8.6900 XPM116 B

ANSXnLY2…Sd25TjkD

67b5010f7379b3…053dce3f166fa8

1 in → 2 out8.6500 XPM226 B

ARVcDJZA…Xc3b7bBe APaYVt8e…rPF99zd2

78da413dbd8c0a…0c6d9434d8eb93

2 in → 2 out10.7339 XPM375 B

Ae9drWdk…FnLTm9Pn AXTUHdJZ…v1ocAiMf

2d5ce7ef13986c…02cf7bc3bba2bc

1 in → 2 out7.6210 XPM226 B

AXJKnSrA…trv2K3WF APCDNTB3…ykwyrxY8

e6dd4c8fde94bb…6c8c439022ac2e

1 in → 2 out7.5578 XPM225 B

AJ5iacfG…vqqvBkuv AYccseR6…53LPVtb8

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.

3.955 × 10⁹⁶(97-digit number)

39554813727101547659…56856759450248565759

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

3.955 × 10⁹⁶(97-digit number)

39554813727101547659…56856759450248565759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.955 × 10⁹⁶(97-digit number)

39554813727101547659…56856759450248565761

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

7.910 × 10⁹⁶(97-digit number)

79109627454203095319…13713518900497131519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.910 × 10⁹⁶(97-digit number)

79109627454203095319…13713518900497131521

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

1.582 × 10⁹⁷(98-digit number)

15821925490840619063…27427037800994263039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.582 × 10⁹⁷(98-digit number)

15821925490840619063…27427037800994263041

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

3.164 × 10⁹⁷(98-digit number)

31643850981681238127…54854075601988526079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.164 × 10⁹⁷(98-digit number)

31643850981681238127…54854075601988526081

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

6.328 × 10⁹⁷(98-digit number)

63287701963362476255…09708151203977052159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.328 × 10⁹⁷(98-digit number)

63287701963362476255…09708151203977052161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.265 × 10⁹⁸(99-digit number)

12657540392672495251…19416302407954104319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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