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Block #277,244

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/27/2013, 12:11:12 PM Β· Difficulty 9.9657 Β· 6,532,118 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
77f83eceb86945d1b9265fd2a7ebf59f8094b9ee7f5e1e6d23a9396b416afbfb
View on Chainz β†—

Height

#277,244

Difficulty

9.965663

Transactions

2

Size

688 B

Version

2

Bits

09f735a9

Nonce

127,543

Timestamp

11/27/2013, 12:11:12 PM

Confirmations

6,532,118

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e705fd740b5621df23547a2a415a8d4404d71010dbe0103d28b72ee394574987
Transactions (2)
Coinbase22206df1888642…16b558f7e535eb
1 in β†’ 1 out10.0600 XPM110 B
AeKNrjNj…1NEq95Ta
67221efbb409f7…04412bfb2d2c6f
3 in β†’ 1 out393.9000 XPM487 B
AH5JBULi…B2SdvBYp
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.

2.756 Γ— 10⁹⁷(98-digit number)
27568437311265480951…61254715502974463999
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
2.756 Γ— 10⁹⁷(98-digit number)
27568437311265480951…61254715502974463999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.756 Γ— 10⁹⁷(98-digit number)
27568437311265480951…61254715502974464001
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
5.513 Γ— 10⁹⁷(98-digit number)
55136874622530961903…22509431005948927999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.513 Γ— 10⁹⁷(98-digit number)
55136874622530961903…22509431005948928001
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
1.102 Γ— 10⁹⁸(99-digit number)
11027374924506192380…45018862011897855999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.102 Γ— 10⁹⁸(99-digit number)
11027374924506192380…45018862011897856001
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
2.205 Γ— 10⁹⁸(99-digit number)
22054749849012384761…90037724023795711999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.205 Γ— 10⁹⁸(99-digit number)
22054749849012384761…90037724023795712001
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
4.410 Γ— 10⁹⁸(99-digit number)
44109499698024769522…80075448047591423999
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:57,718,964 XPMΒ·at block #6,809,361 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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