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Block #155,009

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/8/2013, 1:26:21 AM Β· Difficulty 9.8649 Β· 6,639,885 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5b92c0db117d0ee8f7f78e3a2e065ce73ce87b1ccb8c9eb77ed8df9f8dbb2c72
View on Chainz β†—

Height

#155,009

Difficulty

9.864946

Transactions

1

Size

198 B

Version

2

Bits

09dd6d14

Nonce

78,881

Timestamp

9/8/2013, 1:26:21 AM

Confirmations

6,639,885

Mined by

⛏️ P2SHAJn9y9WvUy9mvP3JMmTsGHrigbG4raUX4o

Merkle Root

4f54bb5f000feb88cfdd8b9bb9b2203f7e8c264c2ef6991f00343b983931a16d
Transactions (1)
Coinbase4f54bb5f000feb…343b983931a16d
1 in β†’ 1 out10.2600 XPM109 B
AJn9y9Wv…G4raUX4o
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.

4.115 Γ— 10⁹²(93-digit number)
41157142732264902388…31543934353520289199
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
4.115 Γ— 10⁹²(93-digit number)
41157142732264902388…31543934353520289199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.115 Γ— 10⁹²(93-digit number)
41157142732264902388…31543934353520289201
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
8.231 Γ— 10⁹²(93-digit number)
82314285464529804776…63087868707040578399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.231 Γ— 10⁹²(93-digit number)
82314285464529804776…63087868707040578401
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
1.646 Γ— 10⁹³(94-digit number)
16462857092905960955…26175737414081156799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.646 Γ— 10⁹³(94-digit number)
16462857092905960955…26175737414081156801
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
3.292 Γ— 10⁹³(94-digit number)
32925714185811921910…52351474828162313599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.292 Γ— 10⁹³(94-digit number)
32925714185811921910…52351474828162313601
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
6.585 Γ— 10⁹³(94-digit number)
65851428371623843821…04702949656324627199
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:57,603,188 XPMΒ·at block #6,794,893 Β· updates every 60s
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