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Block #856,146

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2014, 8:53:04 PM Β· Difficulty 10.9682 Β· 5,958,042 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2ddff4309225e8df1747ebd139abbace12f93ca3146822fc3d5aacfb556840d5
View on Chainz β†—

Height

#856,146

Difficulty

10.968212

Transactions

2

Size

433 B

Version

2

Bits

0af7dcc0

Nonce

349,974,029

Timestamp

12/16/2014, 8:53:04 PM

Confirmations

5,958,042

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

021beb95975d24a1b57094c97a692ecd6813b66f645c8c9831811a27a5b4b5ee
Transactions (2)
Coinbase00fe5f83e5e500…47d21c69e9f2b0
1 in β†’ 1 out8.3150 XPM116 B
ANSXnLY2…Sd25TjkD
ab9c06a5153a65…affbd72614ed68
1 in β†’ 2 out0.0611 XPM226 B
AWod5Yxd…RDDz8We5AYedMKyr…2GKTCWhs
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.

3.256 Γ— 10⁹⁢(97-digit number)
32561011531624305149…35029295769804799999
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
3.256 Γ— 10⁹⁢(97-digit number)
32561011531624305149…35029295769804799999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.256 Γ— 10⁹⁢(97-digit number)
32561011531624305149…35029295769804800001
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
6.512 Γ— 10⁹⁢(97-digit number)
65122023063248610299…70058591539609599999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.512 Γ— 10⁹⁢(97-digit number)
65122023063248610299…70058591539609600001
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
1.302 Γ— 10⁹⁷(98-digit number)
13024404612649722059…40117183079219199999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.302 Γ— 10⁹⁷(98-digit number)
13024404612649722059…40117183079219200001
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
2.604 Γ— 10⁹⁷(98-digit number)
26048809225299444119…80234366158438399999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.604 Γ— 10⁹⁷(98-digit number)
26048809225299444119…80234366158438400001
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
5.209 Γ— 10⁹⁷(98-digit number)
52097618450598888239…60468732316876799999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.209 Γ— 10⁹⁷(98-digit number)
52097618450598888239…60468732316876800001
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
1.041 Γ— 10⁹⁸(99-digit number)
10419523690119777647…20937464633753599999
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:57,757,577 XPMΒ·at block #6,814,187 Β· updates every 60s
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