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Block #248,037

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/7/2013, 3:31:17 AM Β· Difficulty 9.9654 Β· 6,562,992 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4de4be03539d01b1fffe779113e5fac3dac0ebc6f3db42cc3dd17976882c73f6
View on Chainz β†—

Height

#248,037

Difficulty

9.965387

Transactions

2

Size

426 B

Version

2

Bits

09f7239c

Nonce

324,921

Timestamp

11/7/2013, 3:31:17 AM

Confirmations

6,562,992

Mined by

⛏️ P2SHAJv3daGNcNsrxatat8xgVPX4VP8T4HT9Yc

Merkle Root

c52b22ff97c21c14284f924726041944d55fc90ff3e641c468e87077bd1cec14
Transactions (2)
Coinbase1d21d3d45c95e5…4c82af2b11fb87
1 in β†’ 1 out10.0600 XPM109 B
AJv3daGN…8T4HT9Yc
d695921059a309…8ddd1993b481d7
1 in β†’ 2 out4.0078 XPM226 B
AW246M2J…N27HNm8dAJs2PVRi…DCakvMvn
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.

4.805 Γ— 10⁹⁷(98-digit number)
48052869486557601986…85561237125178982399
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
4.805 Γ— 10⁹⁷(98-digit number)
48052869486557601986…85561237125178982399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.805 Γ— 10⁹⁷(98-digit number)
48052869486557601986…85561237125178982401
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
9.610 Γ— 10⁹⁷(98-digit number)
96105738973115203972…71122474250357964799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.610 Γ— 10⁹⁷(98-digit number)
96105738973115203972…71122474250357964801
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
1.922 Γ— 10⁹⁸(99-digit number)
19221147794623040794…42244948500715929599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.922 Γ— 10⁹⁸(99-digit number)
19221147794623040794…42244948500715929601
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
3.844 Γ— 10⁹⁸(99-digit number)
38442295589246081589…84489897001431859199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.844 Γ— 10⁹⁸(99-digit number)
38442295589246081589…84489897001431859201
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
7.688 Γ— 10⁹⁸(99-digit number)
76884591178492163178…68979794002863718399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.688 Γ— 10⁹⁸(99-digit number)
76884591178492163178…68979794002863718401
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:57,732,340 XPMΒ·at block #6,811,028 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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