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Block #662,773

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/4/2014, 9:32:01 PM Β· Difficulty 10.9569 Β· 6,154,612 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
24200484bc4e7c1033659f7daf479cd3fd8bed8b11f2ba70408367672dd2098b
View on Chainz β†—

Height

#662,773

Difficulty

10.956882

Transactions

1

Size

207 B

Version

2

Bits

0af4f632

Nonce

738,099,798

Timestamp

8/4/2014, 9:32:01 PM

Confirmations

6,154,612

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2d60c8fbcd1171d420e0ca69ae13912b5c497dcde52ccc12c6f92b3960adf26e
Transactions (1)
Coinbase2d60c8fbcd1171…f92b3960adf26e
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.301 Γ— 10⁹⁷(98-digit number)
43019909817644719672…81114941941154652159
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
4.301 Γ— 10⁹⁷(98-digit number)
43019909817644719672…81114941941154652159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.301 Γ— 10⁹⁷(98-digit number)
43019909817644719672…81114941941154652161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
8.603 Γ— 10⁹⁷(98-digit number)
86039819635289439344…62229883882309304319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.603 Γ— 10⁹⁷(98-digit number)
86039819635289439344…62229883882309304321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.720 Γ— 10⁹⁸(99-digit number)
17207963927057887868…24459767764618608639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.720 Γ— 10⁹⁸(99-digit number)
17207963927057887868…24459767764618608641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
3.441 Γ— 10⁹⁸(99-digit number)
34415927854115775737…48919535529237217279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.441 Γ— 10⁹⁸(99-digit number)
34415927854115775737…48919535529237217281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
6.883 Γ— 10⁹⁸(99-digit number)
68831855708231551475…97839071058474434559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.883 Γ— 10⁹⁸(99-digit number)
68831855708231551475…97839071058474434561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.376 Γ— 10⁹⁹(100-digit number)
13766371141646310295…95678142116948869119
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
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