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Block #662,268

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/4/2014, 1:48:39 PM Β· Difficulty 10.9565 Β· 6,145,102 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
618fced3076ff704639e54dac6d350945afdacd5b1e27f7d655af466e4d67bc2
View on Chainz β†—

Height

#662,268

Difficulty

10.956513

Transactions

3

Size

1.07 KB

Version

2

Bits

0af4de0b

Nonce

1,046,480,936

Timestamp

8/4/2014, 1:48:39 PM

Confirmations

6,145,102

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

46e6270cbc88d11dcf53884fe3244fc001b6b309550ac8d9525a142dcd087af5
Transactions (3)
Coinbase0e21043f40ad85…7eda5ef474592c
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
b9c715f70e4f05…98f31204512708
4 in β†’ 2 out21.1051 XPM668 B
AFz2rifM…sUMiN2yAAaU9J1Lk…4e47uLfq
3cc3e054f738a5…a84ddbe5b0b7e1
1 in β†’ 2 out6.2891 XPM225 B
ASEkR768…35s3LmSuAL4UeCsm…SkEUuU6D
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.

3.051 Γ— 10⁹⁢(97-digit number)
30518285369835524857…09914069858227254399
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
3.051 Γ— 10⁹⁢(97-digit number)
30518285369835524857…09914069858227254399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.051 Γ— 10⁹⁢(97-digit number)
30518285369835524857…09914069858227254401
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
6.103 Γ— 10⁹⁢(97-digit number)
61036570739671049715…19828139716454508799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.103 Γ— 10⁹⁢(97-digit number)
61036570739671049715…19828139716454508801
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
1.220 Γ— 10⁹⁷(98-digit number)
12207314147934209943…39656279432909017599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.220 Γ— 10⁹⁷(98-digit number)
12207314147934209943…39656279432909017601
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
2.441 Γ— 10⁹⁷(98-digit number)
24414628295868419886…79312558865818035199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.441 Γ— 10⁹⁷(98-digit number)
24414628295868419886…79312558865818035201
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
4.882 Γ— 10⁹⁷(98-digit number)
48829256591736839772…58625117731636070399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.882 Γ— 10⁹⁷(98-digit number)
48829256591736839772…58625117731636070401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,702,981 XPMΒ·at block #6,807,369 Β· updates every 60s
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