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Block #164,388

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/14/2013, 3:30:34 PM Β· Difficulty 9.8625 Β· 6,643,091 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a04a764e12015f266bcc83f80a6de3e8b5816fc752f6ecaf09050a130d61d5b6
View on Chainz β†—

Height

#164,388

Difficulty

9.862503

Transactions

1

Size

198 B

Version

2

Bits

09dccd02

Nonce

29,131

Timestamp

9/14/2013, 3:30:34 PM

Confirmations

6,643,091

Mined by

⛏️ P2SHAdDUNTYmz3S4v6JdhjgL2fyWhUv4Zjqa77

Merkle Root

af83644cff2c1539bf0e102a4f36c84c2400e7f68093a91794b6eb3dbe0ae449
Transactions (1)
Coinbaseaf83644cff2c15…b6eb3dbe0ae449
1 in β†’ 1 out10.2700 XPM109 B
AdDUNTYm…v4Zjqa77
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.

1.467 Γ— 10⁹¹(92-digit number)
14673814908926637756…93034694242807915199
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
1.467 Γ— 10⁹¹(92-digit number)
14673814908926637756…93034694242807915199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.467 Γ— 10⁹¹(92-digit number)
14673814908926637756…93034694242807915201
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
2.934 Γ— 10⁹¹(92-digit number)
29347629817853275513…86069388485615830399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.934 Γ— 10⁹¹(92-digit number)
29347629817853275513…86069388485615830401
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
5.869 Γ— 10⁹¹(92-digit number)
58695259635706551027…72138776971231660799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.869 Γ— 10⁹¹(92-digit number)
58695259635706551027…72138776971231660801
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
1.173 Γ— 10⁹²(93-digit number)
11739051927141310205…44277553942463321599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.173 Γ— 10⁹²(93-digit number)
11739051927141310205…44277553942463321601
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
2.347 Γ— 10⁹²(93-digit number)
23478103854282620410…88555107884926643199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.347 Γ— 10⁹²(93-digit number)
23478103854282620410…88555107884926643201
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:57,703,858 XPMΒ·at block #6,807,478 Β· updates every 60s
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