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Block #298,891

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/7/2013, 2:52:01 PM Β· Difficulty 9.9920 Β· 6,526,001 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
badaed81628ea0f39ddb1a005d1c6880bb089a2ada0dae3141dfa1a3a17426e6
View on Chainz β†—

Height

#298,891

Difficulty

9.992035

Transactions

1

Size

200 B

Version

2

Bits

09fdf5fa

Nonce

88,511

Timestamp

12/7/2013, 2:52:01 PM

Confirmations

6,526,001

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e0de6e2ab1dda165dc369379f415693cd7c763313f339c1e425a4e9f2c563bf8
Transactions (1)
Coinbasee0de6e2ab1dda1…5a4e9f2c563bf8
1 in β†’ 1 out10.0000 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.

6.159 Γ— 10⁹⁡(96-digit number)
61591188460783460856…62532242183562175999
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
6.159 Γ— 10⁹⁡(96-digit number)
61591188460783460856…62532242183562175999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.159 Γ— 10⁹⁡(96-digit number)
61591188460783460856…62532242183562176001
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
1.231 Γ— 10⁹⁢(97-digit number)
12318237692156692171…25064484367124351999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.231 Γ— 10⁹⁢(97-digit number)
12318237692156692171…25064484367124352001
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
2.463 Γ— 10⁹⁢(97-digit number)
24636475384313384342…50128968734248703999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.463 Γ— 10⁹⁢(97-digit number)
24636475384313384342…50128968734248704001
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
4.927 Γ— 10⁹⁢(97-digit number)
49272950768626768685…00257937468497407999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.927 Γ— 10⁹⁢(97-digit number)
49272950768626768685…00257937468497408001
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
9.854 Γ— 10⁹⁢(97-digit number)
98545901537253537371…00515874936994815999
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:57,843,217 XPMΒ·at block #6,824,891 Β· updates every 60s
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