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Block #285,267

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/30/2013, 10:43:11 AM Β· Difficulty 9.9840 Β· 6,510,754 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
69d4239536a0046ef4117c86027c90507e35906da9eb014f3a453d9667b57021
View on Chainz β†—

Height

#285,267

Difficulty

9.983997

Transactions

1

Size

199 B

Version

2

Bits

09fbe738

Nonce

7,096

Timestamp

11/30/2013, 10:43:11 AM

Confirmations

6,510,754

Mined by

⛏️ P2SHAcBserkD6iQpWhykYiADwjyXtzansMWqTY

Merkle Root

7df859572cf7eca9676cb615b8efa55cf294d0ad17c590b9e6da88e594814363
Transactions (1)
Coinbase7df859572cf7ec…da88e594814363
1 in β†’ 1 out10.0200 XPM109 B
AcBserkD…ansMWqTY
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.

3.570 Γ— 10⁹⁡(96-digit number)
35701410484902912825…05963579539234562559
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
3.570 Γ— 10⁹⁡(96-digit number)
35701410484902912825…05963579539234562559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.570 Γ— 10⁹⁡(96-digit number)
35701410484902912825…05963579539234562561
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
7.140 Γ— 10⁹⁡(96-digit number)
71402820969805825650…11927159078469125119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.140 Γ— 10⁹⁡(96-digit number)
71402820969805825650…11927159078469125121
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
1.428 Γ— 10⁹⁢(97-digit number)
14280564193961165130…23854318156938250239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.428 Γ— 10⁹⁢(97-digit number)
14280564193961165130…23854318156938250241
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
2.856 Γ— 10⁹⁢(97-digit number)
28561128387922330260…47708636313876500479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.856 Γ— 10⁹⁢(97-digit number)
28561128387922330260…47708636313876500481
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
5.712 Γ— 10⁹⁢(97-digit number)
57122256775844660520…95417272627753000959
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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
Circulating Supply:57,612,260 XPMΒ·at block #6,796,020 Β· updates every 60s
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