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Block #474,770

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/4/2014, 6:47:22 PM Β· Difficulty 10.4566 Β· 6,335,693 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
901f344985a84f92c5e6bc8b72c9b16d653138111cfa9dd17b2b82d199be1d1c
View on Chainz β†—

Height

#474,770

Difficulty

10.456633

Transactions

2

Size

428 B

Version

2

Bits

0a74e5e9

Nonce

19,668

Timestamp

4/4/2014, 6:47:22 PM

Confirmations

6,335,693

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9b943e4f82f89e6b6c00e3fcc1489431923d15d348ed8c0832da4ceb3f78dd74
Transactions (2)
Coinbasead6dfbb341318c…00988c2178dc6e
1 in β†’ 1 out9.1400 XPM110 B
AeKNrjNj…1NEq95Ta
f59e04320ff825…bce3aa105f0fbd
1 in β†’ 2 out29.2520 XPM226 B
AJVJFpz1…Mo1J5bDRAQQ5i1vA…hU3TQJn2
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.

8.280 Γ— 10⁹⁸(99-digit number)
82800339916625397942…08146115740405716359
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
8.280 Γ— 10⁹⁸(99-digit number)
82800339916625397942…08146115740405716359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.280 Γ— 10⁹⁸(99-digit number)
82800339916625397942…08146115740405716361
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
1.656 Γ— 10⁹⁹(100-digit number)
16560067983325079588…16292231480811432719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.656 Γ— 10⁹⁹(100-digit number)
16560067983325079588…16292231480811432721
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
3.312 Γ— 10⁹⁹(100-digit number)
33120135966650159177…32584462961622865439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.312 Γ— 10⁹⁹(100-digit number)
33120135966650159177…32584462961622865441
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
6.624 Γ— 10⁹⁹(100-digit number)
66240271933300318354…65168925923245730879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.624 Γ— 10⁹⁹(100-digit number)
66240271933300318354…65168925923245730881
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
1.324 Γ— 10¹⁰⁰(101-digit number)
13248054386660063670…30337851846491461759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.324 Γ— 10¹⁰⁰(101-digit number)
13248054386660063670…30337851846491461761
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:57,727,792 XPMΒ·at block #6,810,462 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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