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Block #1,634,183

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/18/2016, 4:24:57 PM Β· Difficulty 10.6031 Β· 5,192,778 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
30b07fddc1afe49e9058fca0e8c7e329fd16e872e3203191d51a3a3d52f669b0
View on Chainz β†—

Height

#1,634,183

Difficulty

10.603140

Transactions

2

Size

573 B

Version

2

Bits

0a9a676a

Nonce

184,633,417

Timestamp

6/18/2016, 4:24:57 PM

Confirmations

5,192,778

Mined by

⛏️ P2SHAPKKDUM9nDWkkgVCRhiavTBNWjzk2zRagr

Merkle Root

c5ee16a993715193a7dc015d05b1ea95a06c16b771ff31d495c7e957efdd1f30
Transactions (2)
Coinbase19ac057d1fd25f…aef42edf8434fa
1 in β†’ 1 out8.8900 XPM110 B
APKKDUM9…zk2zRagr
dc8eb46d3bd122…c7904c22f9b567
2 in β†’ 2 out2.0019 XPM373 B
AWs3WAg7…giQushceAHyMf8WP…5mAT1jtq
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.

6.731 Γ— 10⁹⁴(95-digit number)
67310486392770683268…78420465467476019199
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
6.731 Γ— 10⁹⁴(95-digit number)
67310486392770683268…78420465467476019199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.731 Γ— 10⁹⁴(95-digit number)
67310486392770683268…78420465467476019201
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
1.346 Γ— 10⁹⁡(96-digit number)
13462097278554136653…56840930934952038399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.346 Γ— 10⁹⁡(96-digit number)
13462097278554136653…56840930934952038401
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
2.692 Γ— 10⁹⁡(96-digit number)
26924194557108273307…13681861869904076799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.692 Γ— 10⁹⁡(96-digit number)
26924194557108273307…13681861869904076801
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
5.384 Γ— 10⁹⁡(96-digit number)
53848389114216546615…27363723739808153599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.384 Γ— 10⁹⁡(96-digit number)
53848389114216546615…27363723739808153601
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
1.076 Γ— 10⁹⁢(97-digit number)
10769677822843309323…54727447479616307199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.076 Γ— 10⁹⁢(97-digit number)
10769677822843309323…54727447479616307201
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:57,859,864 XPMΒ·at block #6,826,960 Β· updates every 60s
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