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Block #407,666

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/17/2014, 3:32:43 AM Β· Difficulty 10.4278 Β· 6,419,091 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e8b091c4212b5f99580fbeb20b542ef666a1851d211fbcfed915fd2e3e51c0b2
View on Chainz β†—

Height

#407,666

Difficulty

10.427759

Transactions

1

Size

203 B

Version

2

Bits

0a6d819d

Nonce

70,133

Timestamp

2/17/2014, 3:32:43 AM

Confirmations

6,419,091

Mined by

⛏️ P2SHAV7nW757FL5kANJB72JPGfbwE2rR1wGtX6

Merkle Root

1b51bbabf16154bdb7254683db63ccbdb8f22630d9b73b2e417d8a3b45a03064
Transactions (1)
Coinbase1b51bbabf16154…7d8a3b45a03064
1 in β†’ 1 out9.1800 XPM109 B
AV7nW757…rR1wGtX6
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.

2.953 Γ— 10¹⁰⁴(105-digit number)
29534999858293541342…42052941078509035519
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
2.953 Γ— 10¹⁰⁴(105-digit number)
29534999858293541342…42052941078509035519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.953 Γ— 10¹⁰⁴(105-digit number)
29534999858293541342…42052941078509035521
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
5.906 Γ— 10¹⁰⁴(105-digit number)
59069999716587082684…84105882157018071039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.906 Γ— 10¹⁰⁴(105-digit number)
59069999716587082684…84105882157018071041
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
1.181 Γ— 10¹⁰⁡(106-digit number)
11813999943317416536…68211764314036142079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.181 Γ— 10¹⁰⁡(106-digit number)
11813999943317416536…68211764314036142081
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
2.362 Γ— 10¹⁰⁡(106-digit number)
23627999886634833073…36423528628072284159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.362 Γ— 10¹⁰⁡(106-digit number)
23627999886634833073…36423528628072284161
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
4.725 Γ— 10¹⁰⁡(106-digit number)
47255999773269666147…72847057256144568319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.725 Γ— 10¹⁰⁡(106-digit number)
47255999773269666147…72847057256144568321
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:57,858,214 XPMΒ·at block #6,826,756 Β· updates every 60s
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