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Block #367,023

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/19/2014, 7:00:43 PM Β· Difficulty 10.4361 Β· 6,459,505 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f88590ce21edd3d17c4b17c789f8bbb9c8424d4895fbc90e518328b04c6c46d1
View on Chainz β†—

Height

#367,023

Difficulty

10.436101

Transactions

1

Size

200 B

Version

2

Bits

0a6fa454

Nonce

175,378

Timestamp

1/19/2014, 7:00:43 PM

Confirmations

6,459,505

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

8da87fedc3783eb76e18f1527d2f99f90fc7256cb25a233c6012e641693b3a98
Transactions (1)
Coinbase8da87fedc3783e…12e641693b3a98
1 in β†’ 1 out9.1700 XPM110 B
AeKNrjNj…1NEq95Ta
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.

9.126 Γ— 10⁹⁴(95-digit number)
91260154733562009762…39421122125151774719
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
9.126 Γ— 10⁹⁴(95-digit number)
91260154733562009762…39421122125151774719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.126 Γ— 10⁹⁴(95-digit number)
91260154733562009762…39421122125151774721
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
1.825 Γ— 10⁹⁡(96-digit number)
18252030946712401952…78842244250303549439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.825 Γ— 10⁹⁡(96-digit number)
18252030946712401952…78842244250303549441
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
3.650 Γ— 10⁹⁡(96-digit number)
36504061893424803904…57684488500607098879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.650 Γ— 10⁹⁡(96-digit number)
36504061893424803904…57684488500607098881
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
7.300 Γ— 10⁹⁡(96-digit number)
73008123786849607809…15368977001214197759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.300 Γ— 10⁹⁡(96-digit number)
73008123786849607809…15368977001214197761
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
1.460 Γ— 10⁹⁢(97-digit number)
14601624757369921561…30737954002428395519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.460 Γ— 10⁹⁢(97-digit number)
14601624757369921561…30737954002428395521
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:57,856,370 XPMΒ·at block #6,826,527 Β· updates every 60s
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