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Block #2,533,690

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/22/2018, 4:49:25 PM Β· Difficulty 10.9863 Β· 4,309,325 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7ba35cd92c1ff2c5ba12ae6e25c2729c60c04dfd279184f6625cd82ac6a64935
View on Chainz β†—

Height

#2,533,690

Difficulty

10.986281

Transactions

2

Size

1.68 KB

Version

2

Bits

0afc7ce4

Nonce

1,238,340,784

Timestamp

2/22/2018, 4:49:25 PM

Confirmations

4,309,325

Mined by

⛏️ P2SHARW44o1ef5qVuQNMNtyz53AVTNqWJ4gnTK

Merkle Root

cf6dad88a8aebb5aec6f2a6ba204eacffbe7ad9debdcb0aed303148915d866bf
Transactions (2)
Coinbased37adff084a595…c6ab5d039e4e8d
1 in β†’ 1 out8.2900 XPM110 B
ARW44o1e…qWJ4gnTK
b2318a081c589e…0f5fc4eb5f0c3b
10 in β†’ 1 out39.9800 XPM1.49 KB
ASEhqc6y…uiLW8tms
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.

8.743 Γ— 10⁹⁴(95-digit number)
87434987455164059210…55433976336311446719
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
8.743 Γ— 10⁹⁴(95-digit number)
87434987455164059210…55433976336311446719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.743 Γ— 10⁹⁴(95-digit number)
87434987455164059210…55433976336311446721
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
1.748 Γ— 10⁹⁡(96-digit number)
17486997491032811842…10867952672622893439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.748 Γ— 10⁹⁡(96-digit number)
17486997491032811842…10867952672622893441
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
3.497 Γ— 10⁹⁡(96-digit number)
34973994982065623684…21735905345245786879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.497 Γ— 10⁹⁡(96-digit number)
34973994982065623684…21735905345245786881
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
6.994 Γ— 10⁹⁡(96-digit number)
69947989964131247368…43471810690491573759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.994 Γ— 10⁹⁡(96-digit number)
69947989964131247368…43471810690491573761
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
1.398 Γ— 10⁹⁢(97-digit number)
13989597992826249473…86943621380983147519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.398 Γ— 10⁹⁢(97-digit number)
13989597992826249473…86943621380983147521
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:57,988,475 XPMΒ·at block #6,843,014 Β· updates every 60s
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