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Block #245,374

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/5/2013, 10:30:12 AM Β· Difficulty 9.9638 Β· 6,549,544 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f0e0b89d9678b0d7395f9c493db56e0e9033b1fdec194d66f214cf91679889df
View on Chainz β†—

Height

#245,374

Difficulty

9.963839

Transactions

1

Size

200 B

Version

2

Bits

09f6be2c

Nonce

111,376

Timestamp

11/5/2013, 10:30:12 AM

Confirmations

6,549,544

Mined by

⛏️ P2SHAefNmfCCiMUgcSMoZqwmWZgc6ARj9JS3UM

Merkle Root

1df6803826f2163a6455986faaf0c7cca83000737118aba0f906c9d18874886d
Transactions (1)
Coinbase1df6803826f216…06c9d18874886d
1 in β†’ 1 out10.0600 XPM109 B
AefNmfCC…Rj9JS3UM
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.

2.770 Γ— 10⁹⁷(98-digit number)
27705510949770201617…10463053215477995519
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
2.770 Γ— 10⁹⁷(98-digit number)
27705510949770201617…10463053215477995519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.770 Γ— 10⁹⁷(98-digit number)
27705510949770201617…10463053215477995521
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
5.541 Γ— 10⁹⁷(98-digit number)
55411021899540403234…20926106430955991039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.541 Γ— 10⁹⁷(98-digit number)
55411021899540403234…20926106430955991041
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
1.108 Γ— 10⁹⁸(99-digit number)
11082204379908080646…41852212861911982079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.108 Γ— 10⁹⁸(99-digit number)
11082204379908080646…41852212861911982081
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
2.216 Γ— 10⁹⁸(99-digit number)
22164408759816161293…83704425723823964159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.216 Γ— 10⁹⁸(99-digit number)
22164408759816161293…83704425723823964161
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
4.432 Γ— 10⁹⁸(99-digit number)
44328817519632322587…67408851447647928319
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:57,603,383 XPMΒ·at block #6,794,917 Β· updates every 60s
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