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Block #633,578

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2014, 10:07:06 PM Β· Difficulty 10.9640 Β· 6,191,197 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f42cd27b574b5fa8fb2957b93f7020538e3457d3f60c097fa0095c6312630893
View on Chainz β†—

Height

#633,578

Difficulty

10.963958

Transactions

2

Size

433 B

Version

2

Bits

0af6c5f8

Nonce

994,079,645

Timestamp

7/14/2014, 10:07:06 PM

Confirmations

6,191,197

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5325bb56104842fa7545716a37b704b6fb82980e52c9c8362a91b8eb6e27fbbb
Transactions (2)
Coinbase98efdf7aa2f287…03f5738cc4d718
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
0caff4d9c638d3…5afd68e2508ed6
1 in β†’ 2 out6.1424 XPM226 B
AeKNrjNj…1NEq95TaAbz9CAqQ…etH6XVc6
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.

1.359 Γ— 10⁹⁷(98-digit number)
13591603949689507544…54930350597319500799
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
1.359 Γ— 10⁹⁷(98-digit number)
13591603949689507544…54930350597319500799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.359 Γ— 10⁹⁷(98-digit number)
13591603949689507544…54930350597319500801
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
2.718 Γ— 10⁹⁷(98-digit number)
27183207899379015088…09860701194639001599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.718 Γ— 10⁹⁷(98-digit number)
27183207899379015088…09860701194639001601
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
5.436 Γ— 10⁹⁷(98-digit number)
54366415798758030176…19721402389278003199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.436 Γ— 10⁹⁷(98-digit number)
54366415798758030176…19721402389278003201
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
1.087 Γ— 10⁹⁸(99-digit number)
10873283159751606035…39442804778556006399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.087 Γ— 10⁹⁸(99-digit number)
10873283159751606035…39442804778556006401
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
2.174 Γ— 10⁹⁸(99-digit number)
21746566319503212070…78885609557112012799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.174 Γ— 10⁹⁸(99-digit number)
21746566319503212070…78885609557112012801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.349 Γ— 10⁹⁸(99-digit number)
43493132639006424141…57771219114224025599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,842,272 XPMΒ·at block #6,824,774 Β· updates every 60s
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